Would you like to look after? (4)
I believe the answer is:
care
'look after?' is the definition.
(thesaurus)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for care that I've seen before include "Serious attention and thought" , "Mind" , "Have concern or regard" , "Race (anag.)" , "Consideration" .)